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Topological field theory with Haagerup symmetry

Huang, Tzu-Chen and Lin, Ying-Hsuan (2022) Topological field theory with Haagerup symmetry. Journal of Mathematical Physics, 63 (4). Art. No. 042306. ISSN 0022-2488. doi:10.1063/5.0079062.

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We construct a (1 + 1)d topological field theory (TFT) whose topological defect lines (TDLs) realize the transparent Haagerup H₃ fusion category. This TFT has six vacua, and each of the three non-invertible simple TDLs hosts three defect operators, giving rise to a total of 15 point-like operators. The TFT data, including the three-point coefficients and lasso diagrams, are determined by solving all the sphere four-point crossing equations and torus one-point modular invariance equations. We further verify that the Cardy states furnish a non-negative integer matrix representation under TDL fusion. While many of the constraints we derive are not limited to this particular TFT with six vacua, we leave open the construction of TFTs with two or four vacua. Finally, TFTs realizing the Haagerup H₁ and H₂ fusion categories can be obtained by gauging algebra objects. This article makes a modest offering in our pursuit of exotica and the quest for their eventual conformity.

Item Type:Article
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URLURL TypeDescription Paper
Huang, Tzu-Chen0000-0002-8738-7695
Lin, Ying-Hsuan0000-0001-8904-1287
Additional Information:© 2022 Author(s). Published under an exclusive license by AIP Publishing. Submitted: 17 November 2021; Accepted: 27 March 2022; Published Online: 21 April 2022. The authors would like to thank Yuji Tachikawa for suggesting this interesting project, for helpful advice, and for comments on the first draft. The authors also benefited from enlightening discussions with Chi-Ming Chang, Kantaro Ohmori, Sahand Seifnashri, Shu-Heng Shao, and Yifan Wang. This work was supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632. Y.-H.L. was supported by the Simons Collaboration Grant on the Non-Perturbative Bootstrap and by the Sherman Fairchild Foundation. The authors have no conflicts to disclose. Data Availability: The data that support the findings of this study are available within the article.
Group:Walter Burke Institute for Theoretical Physics
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Department of Energy (DOE)DE-SC0011632
Simons FoundationUNSPECIFIED
Sherman Fairchild FoundationUNSPECIFIED
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Issue or Number:4
Record Number:CaltechAUTHORS:20210219-122651478
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Official Citation:Tzu-Chen Huang and Ying-Hsuan Lin , "Topological field theory with Haagerup symmetry", J. Math. Phys. 63, 042306 (2022)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:108128
Deposited By: Joy Painter
Deposited On:19 Feb 2021 20:36
Last Modified:26 Apr 2022 21:28

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